OG详解-OG1 数学1 Q27

The correct answer is  104. An equilateral triangle is a triangle in which all three sides have the same length and all three angles have a measure of 60^º . The height of the triangle, k√3​ , is the length of the altitude from one vertex. The altitude divides the equilateral triangle into two congruent 30-60-90 right triangles, where the altitude is the side across from the 60^º angle in each 30-60- 90 right triangle. Since the altitude has a length of  k√3​, it follows from the properties of 30-60-90 right triangles that the side across from each 30^º angle has a length of  k and each hypotenuse has a length of  2k. In this case, the hypotenuse of each 30-60-90 right triangle is a side of the equilateral triangle;therefore, each side length of the equilateral triangle is  2k. The perimeter of a triangle is the sum of the lengths of each side. It’s given that the perimeter of the equilateral triangle is 624; therefore, 2k +2k +2k = 624 , or 6k = 624 . Dividing both sides of this equation by 6 yields k = 104.